Abstract
We discuss the signature of space–time in the context of the E 11 -conjecture. In this setting, the space–time signature depends on the choice of basis for the “gravitational subalgebra” A 10 , and Weyl transformations connect interpretations with different signatures of space–time. Also the sign of the 4-form gauge field term in the Lagrangian enters as an adjustable sign in a generalized signature. Within E 11 , the combination of space–time signature ( 1 , 10 ) with conventional sign for the 4-form term, appropriate to M-theory, can be transformed to the signatures ( 2 , 9 ) and ( 5 , 6 ) of Hull's M * - and M ′ -theories (as well as ( 6 , 5 ) , ( 9 , 2 ) and ( 10 , 1 ) ) . Theories with other signatures organize in orbits disconnected from these theories. We argue that when taking E 11 seriously as a symmetry algebra, one cannot discard theories with multiple time-directions as unphysical. We also briefly explore links with the SL ( 32 , R ) conjecture.
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